Emerging Technologies in Research: Google Apps and SPSS

Statistics

• Statistics deals with uncertainty & variability
• Statistics turns data into information
• Data -> Information -> Knowledge -> Wisdom
• Statistics is the interpretation of Science
• Statistics is the Art & Science of learning from data

Variable

• Characteristic that may vary from individual to individual

Measurement

• Process of assigning numbers or labels to objects or states in accordance with logically accepted rules

Measurement Scales

• Nominal Scale: Obersvations may be classified into mutually exclusive & exhaustive categories
• Ordinal Scale: Obersvations may be ranked
• Interval Scale: Difference between obersvations is meaningful
• Ratio Scale: Ratio between obersvations is meaningful & true zero point

Descriptive Statistics

• No of observations
• Measures of Central Tendency
• Measures of Dispersion
• Measures of Skewness
• Measures of Kurtosis

Example

Fertilizer (Kg/acre) Production (Bushels/acre)
100 70
200 70
400 80
500 100

Analyze > Descriptive Statistics > Descriptives …

Boxwhisker Diagram

• Pictorial display of five number summary (Minimum, Q1, Q2, Q3 and Maximum)

Example

Yield Variety
5 V1
6 V1
7 V1
15 V2
16 V2
17 V2

Graphs > Legacy Dialogs > Scatter/Boxplot …

Regression Analysis

• Quantifying dependency of a normal response on quantitative explanatory variable(s)

Simple Linear Regression

• Quantifying dependency of a normal response on a quantitative explanatory variable

Example

Fertilizer (Kg/acre) Production (Bushels/acre)
100 70
200 70
400 80
500 100

Graphs > Legacy Dialogs > Scatter/Dot …

Analyze > Regression > Linear …

Fertilizer Yield
0.3 10
0.6 15
0.9 30
1.2 35
1.5 25
1.8 30
2.1 50
2.4 45

Exercise

Weekly Income ($) Weekly Expenditures ($)
80 70
100 65
120 90
140 95
160 110
180 115
200 120
220 140
240 155
260 150

Multiple Linear Regression

• Quantifying dependency of a normal response on two or more quantitative explanatory variables

Example

Fertilizer (Kg) Rainfall (mm) Yield (Kg)
100 10 40
200 20 50
300 10 50
400 30 70
500 20 65
600 20 65
700 30 80

Analyze > Regression > Linear …

Polynomial Regression Analysis

• Quantifying non-linear dependency of a normal response on quantitative explanatory variable(s)

Example

An experiment was conducted to evaluate the effects of different levels of nitrogen. Three levels of nitrogen: 0, 10 and 20 grams per plot were used in the experiment. Each treatment was replicated twice and data is given below:

Nitrogen Yield
0 5
0 7
10 15
10 17
20 9
20 11

Analysis of Variance (ANOVA)

• Comparing means of Normal dependent variable for levels of different factor(s)

Example

Yield Variety
5 V1
6 V1
7 V1
15 V2
16 V2
17 V2

General Linear Model > Univariate …

Yield Variety
5 V1
7 V1
15 V2
17 V2
17 V3
19 V3

Analysis of Covariance (ANCOVA)

• Quantifying dependency of a normal response on quantitative explanatory variable(s)
• Comparing means of Normal dependent variable for levels of different factor(s)

Example

Yield Fert Variety
51 80 V1
52 80 V1
53 90 V1
54 90 V1
56 100 V1
57 100 V1
55 80 V2
56 80 V2
58 90 V2
59 90 V2
62 100 V2
63 100 V2

Correlation Analysis

• Linear Relationship between Quantitative Variables

Simple Correlation Analysis

• Linear Relationship between Two Quantitative Variables
• $\left(X_{1},X_{2}\right)$

Example

Sparrow Wing length (cm) Sparrow Tail length (cm)
10.4 7.4
10.8 7.6
11.1 7.9
10.2 7.2
10.3 7.4
10.2 7.1
10.7 7.4
10.5 7.2
10.8 7.8
11.2 7.7
10.6 7.8
11.4 8.3

Analyze > Correlate > Bivariate …

Partial Correlation Analysis

• Linear Relationship between Quantitative Variables while holding/keeping all other constants
• $\left(X_{1},X_{2}\right)|X_{3}$

Example

Leaf Area (cm^2) Leaf Moisture (%) Total Shoot Length (cm)
72 80 307
174 75 529
116 81 632
78 83 527
134 79 442
95 81 525
113 80 481
98 81 710
148 74 422
42 78 345

Analyze > Correlate > Partial …

Multiple Correlation Analysis

• Linear Relationship between a Quantitative Variable and set of other Quantitative Variables
• $\left(X_{1},\left[X_{2},X_{3}\right]\right)$

Example

Leaf Area (cm^2) Leaf Moisture (%) Total Shoot Length (cm)
72 80 307
174 75 529
116 81 632
78 83 527
134 79 442
95 81 525
113 80 481
98 81 710
148 74 422
42 78 345

Completely Randomized Design (CRD)

• Used when experimental material is homogeneous

Example

The following table shows some of the results of an experiment on the effects of applications of sulphur in reducing scab disease of potatoes. The object in applying sulphur is to increase the acidity of the soil, since scab does not thrive in very acid soil. In addition to untreated plots which serve as a control, 3 amounts of dressing were compared—300, 600, and 900 lb. per acre. Both a fall and a spring application of each amount was tested, so that in all there were seven distinct treatments. The sulphur was spread by hand on the surface of the soil, and then diced into a depth of about 4 inches. The quantity to be analyzed is the “scab index”. That is roughly speaking, the percentage of the surface area of the potato that is infected with scab. It is obtained by examining 100 potatoes at random from each plot, grading each potato on a scale from 0 to 100% infected, and taking the average.

Randomized Complete Block Design (RCBD)

• Used when experimental material is heterogenous in one direction

Example

Yield : Yield of barley, SoilType : Soil Type, and Trt : 5 sources and a control

Latin Square Design

• Used when experimental material is heterogenous in two perpendicular directions

Example

The following table shows the field layout and yield of a 5×5 Latin square experiment on the effect of spacing on yield of millet plants. Five levels of spacing were used. The data on yield (grams/plot) was recorded and is given below: